Turing Degrees

Some articles on turing degrees, turing, degrees:

Recursion Theory - Areas of Research - Relative Computability and The Turing Degrees
... on relative computability, a generalization of Turing computability defined using oracle Turing machines, introduced by Turing (1939) ... An oracle Turing machine is a hypothetical device which, in addition to performing the actions of a regular Turing machine, is able to ask questions ... Informally, a set of natural numbers A is Turing reducible to a set B if there is an oracle machine that correctly tells whether numbers are in A when run with B as the oracle set (in this case, the set A is ...
Theodore Slaman
... Hugh Woodin formulated the Bi-interpretability Conjecture for the Turing degrees, which conjectures that the partial order of the Turing degrees is ... Conjecture is equivalent to there being no nontrivial automorphism of the Turing degrees ... They also exhibited limits on the possible automorphisms of the Turing degrees by showing that any automorphism will be arithmetically definable ...
Recursion Theory - Areas of Research - Automorphism Problems
... of recursively enumerable sets, automorphisms are also studied for the structure of the Turing degrees of all sets as well as for the structure of the Turing degrees of r.e ... both cases, Cooper claims to have constructed nontrivial automorphisms which map some degrees to other degrees this construction has, however, not been verified ...
Structure of The Turing Degrees
... A great deal of research has been conducted into the structure of the Turing degrees ... One general conclusion that can be drawn from the research is that the structure of the Turing degrees is extremely complicated ...

Famous quotes containing the word degrees:

    How have I been able to live so long outside Nature without identifying myself with it? Everything lives, moves, everything corresponds; the magnetic rays, emanating either from myself or from others, cross the limitless chain of created things unimpeded; it is a transparent network that covers the world, and its slender threads communicate themselves by degrees to the planets and stars. Captive now upon earth, I commune with the chorus of the stars who share in my joys and sorrows.
    Gérard De Nerval (1808–1855)